WASHINGTON—President Trump said he is considering measures to bolster the economy, including a possible reduction in capital-gains taxes, and continued to press the Federal Reserve to cut interest rates even as he played down warning signs of a possible slowdown.

“We’re looking at various tax reductions,” Mr. Trump told reporters at the White House on Tuesday. “But I’m looking at that all the time anyway.” He added: “We’re very far from a recession.”

With stock and bond markets signaling in recent weeks that a threat of a downturn from overseas is spreading to the U.S., Mr. Trump said his administration was exploring lowering capital-gains taxes by indexing gains to inflation, which he suggested he could do through regulatory action rather than through Congress. Such a move would likely face immediate court challenges.

Navigating a possible economic downturn would be a particularly thorny issue for Mr. Trump, who has made economic growth under his tenure a central selling point for his 2020 campaign. Administration and campaign aides have privately expressed concern that a slowing economy could complicate his re-election bid, which they already believe will be a tough fight.

Mr. Trump and his advisers on Tuesday said any proposals weren’t a direct response to concerns about a recession, and White House discussions may not lead to any new policies. The president and his aides have frequently said they are considering new economic measures, such as when they suggested new tax cuts ahead of the 2018 elections. No such measures have come to fruition since tax cuts the president signed into law in December 2017.

The government typically uses three tools to help ward off a recession. But with these already in play to help prop up the economy, the Trump administration may have reason to worry.

It isn’t clear a capital-gains tax cut would bolster the economy. An analysis by the Tax Policy Center, a nonpartisan Washington research group run by a former Obama administration official, found that a lower capital-gains tax rate doesn’t substantially spur economic growth.

Under current law, investors pay taxes on their nominal capital gains, meaning that someone who in 1990 bought $100,000 of stock that is now worth $1 million would pay taxes on $900,000 in capital gains, even though some of that gain is due to inflation.

Allowing taxpayers to adjust their cost basis for inflation might encourage people to sell long-held assets. But it would also reduce taxes by about $100 billion over a decade, according to the Penn-Wharton Budget Model, with most of the benefits going to high-income households.

Lawrence Kudlow, a top White House economic adviser, has long supported the idea of indexing, as have other conservatives who say it would lift stocks and encourage households to invest more. Treasury Secretary
Steven Mnuchin
so far hasn’t embraced unilaterally indexing capital-gains taxes, administration officials said. Mr. Trump hasn’t issued any directives, and the Treasury Department hasn’t proposed any changes.

The Trump administration’s belief that it has the authority to unilaterally index gains to inflation conflicts with a 1992 opinion in which the Justice Department’s Office of Legal Counsel concluded that Treasury lacked the authority to define the word “cost” to include inflationary gains. The attorney general at the time,
William Barr,
is again the attorney general.

Democrats in Congress have shown little support for further tax cuts and have warned that indexing without congressional approval is illegal and would simply benefit old investments without necessarily spurring new growth.

Veterans of previous administrations questioned the White House’s publicly floating various policy proposals to address the economy. “It’s not a particularly coherent economic and political strategy,” said Douglas Holtz-Eakin, former chief economist for the White House Council of Economic Advisers under President
George W. Bush.
Mr. Holtz-Eakin, who doesn’t think a downturn is imminent, criticized the “sort of public floating of these weird ideas.”

The president on Tuesday also continued to press the Fed to reduce interest rates, reiterating his call for the central bank to cut its benchmark rate by at least a percentage point—a move that would typically be considered only when the U.S. economy is severely struggling. He added that the rate reductions could be made in several steps.

Such a rate cut hasn’t happened since the global financial crisis in late 2008. Some of Mr. Trump’s advisers have privately encouraged him to continue criticizing the Fed in an effort to place blame on the central bank instead of the president’s policies.

The economic expansion this summer became the longest on record in the U.S. Unemployment is exceptionally low and consumer spending appears robust, but warning signs are flashing. Growth in economic output slowed to a 2.1% annual rate in the second quarter from a 3.5% annual rate in the second quarter of 2018.

Among other possible steps to bolster the economy, Mr. Trump said Tuesday he has been thinking about a payroll-tax cut for “a long time,” but said nothing was imminent on that front—a day after White House officials said such a move wasn’t under consideration. Payroll taxes, which are separate from the federal income tax, fund Medicare and Social Security, and a reduction would boost workers’ take-home pay.

Some administration officials have been concerned about the effect of tariffs on the U.S. economy, and economic experts say Mr. Trump’s trade war with China has alarmed Americans about the future of trade and that the changing cost of doing business is causing trepidation about investment.

Mr. Trump is unlikely to reverse tariffs on China, which he has said are helping pressure Beijing in negotiations over a trade deal with the U.S. Last week, however, he opted to back off a Sept. 1 deadline for some new tariffs on Chinese imports, telling reporters he was doing so to avoid any impact on U.S. shoppers during the holiday season.

WSJ's Gerald F. Seib explains three ways the delay of new tariffs on Chinese goods might benefit the U.S. economy.

The exploration of possible measures to boost the economy comes as White House officials have publicly said they see no warning signs. Vice President
Mike Pence,
speaking at the Detroit Economic Club luncheon in Detroit on Monday, criticized “naysayers” for expressing concern about the state of the economy.

Democrats have said the president’s economic policies have heightened the odds of a recession. In Prole, Iowa, presidential candidate
Joe Biden
accused Mr. Trump of conducting an “irresponsible tariff war” that he said was hurting American farmers. The former vice president said the U.S. should be “raising the capital-gains tax and cutting taxes for middle-class people.”

On Tuesday, the White House held a call with state and local officials that the administration had advertised as a briefing on the U.S. economy with Mr. Kudlow, director of the National Economic Council.

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Instead, in the roughly 10-minute call, the acting chairman of the Council of Economic Advisers, Tomas Philipson, heaped praise on the economy and touted what he said were the effects of 2017 tax cuts on economic growth. Mr. Philipson also cited low state unemployment numbers and wage growth, according to a person who listened to the call. He didn’t take questions.

Corrections & Amplifications Under current law, investors pay taxes on their nominal capital gains, meaning that someone who in 1990 bought $100,000 of stock that is now worth $1 million would pay taxes on $900,000 in capital gains, even though some of that gain is due to inflation. An earlier version of this article incorrectly stated $900,000 million.